Complete Question
The options for the above question is
a There is not sufficient evidence to warrant rejection of the claim.
b There is sufficient evidence to warrant rejection of the claim.
c There is sufficient evidence to support the claim.
d There is not sufficient evidence to support the claim.
Answer:
Option A is correct
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu =[/tex]$47,500
The sample size is [tex]n = 86[/tex]
The sample mean is [tex]\= x =[/tex]$48,061
The standard deviation is [tex]\sigma =[/tex]$2,351
The level of significance is [tex]\alpha = 0.02[/tex]
The null hypothesis is
[tex]H_o : \mu =[/tex]$47,500
The alternative hypothesis is
[tex]H_a : \mu \ne[/tex] $47,500
The critical value of [tex]\alpha[/tex] from the t-Distribution table is [tex]Z_{\frac{\alpha }{2} } = 2.326[/tex]
Now the test statistics is mathematically evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{48061 - 47500 }{\frac{2351}{\sqrt{86} } }[/tex]
[tex]t = 2.21[/tex]
Now from the values obtained we can see that
[tex]Z_{\frac{\alpha }{2} } > t[/tex]
hence we fail to reject the null hypothesis
Hence there is not sufficient evidence to warrant rejection of the claim
